# Divisors Identity

Number Theory Level 4

Inclusive of 1 and itself, let $$d_1,d_2,\ldots,d_n$$ denote the distinct positive divisors of positive integer $$N$$. Given that $$\displaystyle \sum_{m=1}^n d_m = 4056 \times18$$ and $$\displaystyle \sum_{m=1}^n \frac1{d_m} = \frac{4056}{25\times55}$$, find the value of $$N$$.

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